Visually, the "extreme" outliers in the following graph are somewhat obvious:




  • T - Set of all temperatures
  • Y - Set of all years
  • ΣT - Sum of temperatures.
  • ΣY - Sum of years.
  • N - Number of elements
  • T(n) - Temperature of the nth element in the temperature set

How do you determine if T(n) is an outlier?

Related Sites

The math on some of these sites is a bit above my understanding:

Many thanks!

  • $\begingroup$ Although I find the question to be interesting and profound, I removed the set-theory tag, since I don't find it applicable. Perhaps the question could be further retagged? $\endgroup$ – Joel David Hamkins May 10 '10 at 2:40
  • 2
    $\begingroup$ If you are looking for practical approaches to outlier removal, you might like to read the answers to mathoverflow.net/questions/6819/…. If you are interested in a philosophical discussion about when it is appropriate to remove outliers (if it ever is) then it appears that Joel might be interested in such a discussion -). $\endgroup$ – Robby McKilliam May 10 '10 at 3:41

I might suggest LTS, the Least Trimmed Squares, approach. there is code in fortran and matlab, the latter called fastlts, both produced, I believe, by Rousseuw's group. The method essentially minimizes the error of fit for a proportion of the data points, with the rest (outliers) ignored. The outliers are found by something like the Minimum Volume Ellipsoid method (roughly, find the ellipsoid of minimum volume containing 1/2 the points).


| cite | improve this answer | |

Douglas Hawkins' book Identification of Outliers is not up to date unless it's been edited since last I looked, but it might give you some idea of the issues involved, no awareness of which is apparent in Steven Pav's answer.

(BTW, I'd have called this a one-variable linear regression; I was surprised to see what it was, given the subject heading.)

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.